diff --git a/lib/compress.js b/lib/compress.js
index 4a91e17e..473fd38c 100644
--- a/lib/compress.js
+++ b/lib/compress.js
@@ -6321,7 +6321,7 @@ Compressor.prototype.compress = function(node) {
 
     function to_class_expr(defcl, drop_name) {
         var cl = make_node(AST_ClassExpression, defcl, defcl);
-        cl.name = drop_name ? null : make_node(AST_SymbolClass, defcl.name, defcl.name);
+        if (cl.name) cl.name = drop_name ? null : make_node(AST_SymbolClass, cl.name, cl.name);
         return cl;
     }
 
@@ -6697,9 +6697,9 @@ Compressor.prototype.compress = function(node) {
                     log(node.name, "Dropping unused class {name}");
                     def.eliminated++;
                     descend(node, tt);
-                    if (parent instanceof AST_ExportDefault) return to_class_expr(node, true);
-                    var trimmed = node.drop_side_effect_free(compressor, true);
-                    if (trimmed === node) trimmed = to_class_expr(node, true);
+                    var trimmed = to_class_expr(node, true);
+                    if (parent instanceof AST_ExportDefault) return trimmed;
+                    trimmed = trimmed.drop_side_effect_free(compressor, true);
                     if (trimmed) return make_node(AST_SimpleStatement, node, { body: trimmed });
                     return in_list ? List.skip : make_node(AST_EmptyStatement, node);
                 }
@@ -8204,6 +8204,16 @@ Compressor.prototype.compress = function(node) {
             }
             return changed && exp.clone();
         }
+        function assign_this_only(fn, compressor) {
+            fn.new = true;
+            var result = all(fn.body, function(stat) {
+                return !stat.has_side_effects(compressor);
+            }) && all(fn.argnames, function(argname) {
+                return !argname.match_symbol(return_false);
+            }) && !(fn.rest && fn.rest.match_symbol(return_false));
+            fn.new = false;
+            return result;
+        }
         def(AST_Call, function(compressor, first_in_statement) {
             var self = this;
             if (self.is_expr_pure(compressor)) {
@@ -8253,17 +8263,8 @@ Compressor.prototype.compress = function(node) {
             self.call_only = true;
             return self;
         });
-        function assign_this_only(fn, compressor) {
-            fn.new = true;
-            var result = all(fn.body, function(stat) {
-                return !stat.has_side_effects(compressor);
-            }) && all(fn.argnames, function(argname) {
-                return !argname.match_symbol(return_false);
-            }) && !(fn.rest && fn.rest.match_symbol(return_false));
-            fn.new = false;
-            return result;
-        }
-        function drop_class(self, compressor, first_in_statement) {
+        def(AST_ClassExpression, function(compressor, first_in_statement) {
+            var self = this;
             var exprs = [], values = [];
             var props = self.properties;
             for (var i = 0; i < props.length; i++) {
@@ -8286,11 +8287,11 @@ Compressor.prototype.compress = function(node) {
             if (exprs) first_in_statement = false;
             values = trim(values, compressor, first_in_statement);
             if (!exprs) {
-                if (!base && !values) return null;
+                if (!base && !values && !self.name) return null;
                 exprs = [];
             }
-            if (base || !compressor.has_directive("use strict")) {
-                var node = to_class_expr(self, true);
+            if (base || self.name || !compressor.has_directive("use strict")) {
+                var node = to_class_expr(self);
                 if (!base) node.extends = null;
                 node.properties = [];
                 if (values) {
@@ -8319,12 +8320,6 @@ Compressor.prototype.compress = function(node) {
                 args: [],
             }));
             return make_sequence(self, exprs);
-        }
-        def(AST_ClassExpression, function(compressor, first_in_statement) {
-            var self = this;
-            var name = self.name;
-            if (name && name.fixed_value() !== self && name.definition().references.length > 0) return self;
-            return drop_class(self, compressor, first_in_statement);
         });
         def(AST_Conditional, function(compressor) {
             var consequent = this.consequent.drop_side_effect_free(compressor);
@@ -8365,9 +8360,6 @@ Compressor.prototype.compress = function(node) {
             return exprs.length == 0 ? null : make_sequence(this, exprs);
         });
         def(AST_Constant, return_null);
-        def(AST_DefClass, function(compressor, first_in_statement) {
-            return drop_class(this, compressor, first_in_statement);
-        });
         def(AST_Dot, function(compressor, first_in_statement) {
             var expr = this.expression;
             if (expr.may_throw_on_access(compressor)) return this;
@@ -11673,7 +11665,7 @@ Compressor.prototype.compress = function(node) {
             if (fixed && (state = self.fixed || def.fixed).should_replace !== false) {
                 var ev, init;
                 if (fixed instanceof AST_This) {
-                    if (!is_funarg(def) && same_scope(def)) init = fixed;
+                    if (!is_funarg(def) && same_scope(def) && !cross_class(def)) init = fixed;
                 } else if ((ev = fixed.evaluate(compressor, true)) !== fixed
                     && typeof ev != "function"
                     && (ev === null
@@ -11715,6 +11707,14 @@ Compressor.prototype.compress = function(node) {
         }
         return self;
 
+        function cross_class(def) {
+            var scope = self.scope;
+            while (scope !== def.scope) {
+                if (scope instanceof AST_Class) return true;
+                scope = scope.parent_scope;
+            }
+        }
+
         function has_symbol_ref(value) {
             var found;
             value.walk(new TreeWalker(function(node) {
diff --git a/test/compress/classes.js b/test/compress/classes.js
index c55b41ff..4e613fc4 100644
--- a/test/compress/classes.js
+++ b/test/compress/classes.js
@@ -2038,6 +2038,32 @@ issue_5015_3: {
         });
         console.log("PASS");
     }
+    expect: {
+        "use strict";
+        (class A {});
+        console.log("PASS");
+    }
+    expect_stdout: "PASS"
+    node_version: ">=4"
+}
+
+issue_5015_4: {
+    options = {
+        reduce_vars: true,
+        sequences: true,
+        side_effects: true,
+        toplevel: true,
+        unused: true,
+    }
+    input: {
+        "use strict";
+        (class A {
+            static f() {
+                return A;
+            }
+        });
+        console.log("PASS");
+    }
     expect: {
         "use strict";
         console.log("PASS");
@@ -2336,3 +2362,90 @@ issue_5142: {
     expect_stdout: "PASS"
     node_version: ">=12"
 }
+
+issue_5294_1: {
+    options = {
+        reduce_vars: true,
+        side_effects: true,
+        toplevel: true,
+    }
+    input: {
+        (class A {
+            static p = console.log(typeof A);
+        });
+    }
+    expect: {
+        (class A {
+            static c = console.log(typeof A);
+        });
+    }
+    expect_stdout: "function"
+    node_version: ">=12"
+}
+
+issue_5294_2: {
+    options = {
+        reduce_vars: true,
+        side_effects: true,
+        toplevel: true,
+    }
+    input: {
+        class A {
+            static p = console.log(typeof A);
+        }
+    }
+    expect: {
+        class A {
+            static p = console.log(typeof A);
+        }
+    }
+    expect_stdout: "function"
+    node_version: ">=12"
+}
+
+issue_5294_3: {
+    options = {
+        reduce_vars: true,
+        toplevel: true,
+        unused: true,
+    }
+    input: {
+        var a = this;
+        (class A {
+            static p = console.log(a === A ? "FAIL" : "PASS");
+        });
+    }
+    expect: {
+        var a = this;
+        (class A {
+            static p = console.log(a === A ? "FAIL" : "PASS");
+        });
+    }
+    expect_stdout: "PASS"
+    node_version: ">=12"
+}
+
+issue_5294_4: {
+    options = {
+        reduce_vars: true,
+        toplevel: true,
+        unused: true,
+    }
+    input: {
+        (class A {
+            static p = function() {
+                var a = this;
+                console.log(a === A ? "FAIL" : "PASS");
+            }();
+        });
+    }
+    expect: {
+        (class A {
+            static p = function() {
+                console.log(this === A ? "FAIL" : "PASS");
+            }();
+        });
+    }
+    expect_stdout: "PASS"
+    node_version: ">=12"
+}